(1) Field of the Invention
The present invention generally relates to monitoring belief conflicts when belief functions are combined, and more particularly, to conflict monitoring without the need for normalization of the combined beliefs.
(2) Description of Related Art
A system may have multiple information sources that are used to make a decision. The well-known Dempster-Shafer (D-S) theory of evidential reasoning provides a mechanism of combining information from different, and possibly contradictory, information sources to allow a system to make proper decisions. The D-S theory uses explicit representations of ignorance and conflict to avoid the shortcomings of classical Bayesian probability calculus. The D-S theory uses belief functions (also known as basic probability assignments or BPAs), which are generalizations of discrete probability functions used in Bayesian probability calculus. In D-S theory, BPAs represent the distribution of probability mass in a system (i.e., how strongly something is believed, based on the information that has been provided). The Dempster-Shafer theory therefore, is based on obtaining degrees of belief for one question from subjective probabilities for a related question, and uses the Dempster's rule for combining such degrees of belief when they are based on independent items or evidence.
Conflict arises when combined belief functions contradict one another. Conflict monitoring is a basic approach to analyzing the aggregate beliefs of input beliefs in a belief inference system. It allows for a better analysis of beliefs, and improved understanding of the belief inference processes. With today's methods, costly computational operations and methodologies are required to perform conflict monitoring. That is, monitoring must be performed in every operation of a belief inference system to determine conflict. Conflict monitoring involves the performance of normalization, step-by-step, for every combination of belief functions. Normalization is the scaling of combined probabilities in BPA's to add up to one. In general, when probabilities in BPA's are combined, they must add up to one, which is a fundamental definition for the D-S theory. During the process of combining BPA's, the resulting combined BPA numbers may not add up to one because some possibilities may have been eliminated during the process, requiring normalization of the combined BPA's.
Conflict may be defined as the mass assigned to the null set during a combination operation. Conflict C and the normalization factor (k) (included in Shafer's definition of the Dempster's Rule of Combination) have a simple mathematical relationship represented by k=1−C. Normally, belief inference systems using D-S do not need to normalize the combined BPAs during repeated combination operations since the normalization operation can be delayed to when an output is required. Hence, the marginal BPAs of the system for the outputs are normalized only when a marginal BPA is requested. This approach reduces the number of computations that are required in performing the normalization after every combination. However, this prior art approach only reveals the combined total conflict in the combined result and ignores the different types of intermediate conflicts that exist within the intermediate combined BPAs. Therefore, in order to keep track of the “intermediate” conflicts at each combination, today's systems must perform costly normalization computations at every step.
In light of the current state of the art and the drawbacks to current systems and methods mentioned above, a need exists for a method and a system that would allow monitoring of conflicts resulting from combining BPAs without performing the associated costly normalization computations at every step of combination.